# Bayesian Trend Filtering

arXiv: https://arxiv.org/abs/1505.07710 · HTML: https://mlsanity.com/paper/1505.07710/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2015.

## Built on by (most cited first, 1 of 1)

- [Modelling Heterogeneity Using Bayesian Structured Sparsity](https://mlsanity.com/paper/2103.15919/) (2021)

## Abstract (arXiv)

We develop a fully Bayesian hierarchical model for trend filtering, itself a new development in nonparametric, univariate regression. The framework more broadly applies to the generalized lasso, but focus is on Bayesian trend filtering. We compare two shrinkage priors, double exponential and generalized double Pareto. A simulation study, comparing Bayesian trend filtering to the original formulation and a number of other popular methods shows our method to improve estimation error while maintaining if not improving coverage probability. Two time series data sets demonstrate Bayesian trend filtering's robustness to possible violations of its assumptions.